For the pizza dough: Heat 1/4 cup of the olive oil and the garlic in a small saucepan over medium-low heat until the garlic is softened but not browned, about 5 minutes. Stir in 1/2 teaspoon pepper. Cool slightly.
Whisk the water and sugar in a bowl; sprinkle the yeast over top. Set aside until foamy, about 10 minutes. Stir in the olive oil-garlic mixture.
Whisk the flour and 2 teaspoons salt in a large bowl. Make a well in the center of the flour and pour in the yeast mixture. Gradually stir with a wooden spoon to make a rough dough.
Turn the dough out onto a lightly floured surface. Knead until smooth and elastic, about 5 minutes, dusting with more flour as necessary. Form into a large ball. Brush a large bowl with olive oil, add the dough and turn to coat. Cover tightly with plastic wrap and set aside at room temperature until doubled in size, about 1 hour.
Meanwhile, adjust an oven rack to the lowest position and preheat to 220°C. Put a baking sheet on the rack to heat up while the dough rises. (The baking sheet should be the same size or slightly larger than the baking sheet that you will later form the dough on.)
Once the dough has doubled in size, brush a rimmed baking sheet generously with half of the remaining olive oil. Put the dough onto the oiled baking sheet and stretch and pat evenly into the pan, making sure that it reaches the edges. Use your fingertips to make dimples all over the dough. Brush with the remaining olive oil and sprinkle lightly with salt. Arrange the tomato slices on the pizza in a single layer, making sure that each bite will have a piece of tomato. Sprinkle the tomatoes lightly with salt. Place the baking sheet with the dough directly on top of the preheated baking sheet in the oven (this helps with a crispy crust). Bake for 15 minutes. Remove the baking sheets and sprinkle the Parmesan over the dough. Continue to bake until the dough is golden brown and the cheese is melted, 10 to 15 minutes
While the pizza is baking, make the Caesar dressing: Whisk together the lemon zest and juice, egg yolk, anchovies, garlic and honey in a large bowl. Slowly whisk in the olive oil, season with 1/4 teaspoon salt and a few grinds of pepper.
Remove the pizza from the oven and transfer to a large platter or cutting board. Toss the romaine with the dressing. Season with additional salt and pepper if needed. Top the pizza with the salad. Use a vegetables peeler to shave ribbons of Parmesan over the salad. Drizzle with olive oil, cut into pieces and serve.
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